1. Field of the Invention
The present invention relates to a rotor for a Roots vacuum pump with two identical rotors having basically a figure-of-eight profile contour composed of four profile sections at the base and four profile sections at the top.
2. Description of the Related Art
Roots vacuum pumps of this type have found wide spread use. The rotary motion of the rotors which rotate at the same speed is synchronized by a gear so that they are near to one another and to the housing without actual contact. The rotors are not subject to mechanical wear and may be operated at high speeds. The gap which remains between the wall of the housing and the rotors, and between the rotors themselves is usually in the order of several tenths of a millimeter.
Shown in FIGS. 1-4 are sections through known rotors or pairs of rotors of Roots vacuum pumps of the aforementioned type. Shown in FIG. 1a is a rotor profile contour developed from an involute. The rotor profile contour according to FIG. 1b is disclosed in CH-PS 389 817 (FIGS. 3, 6, "straight" rotors). The profile contour according to FIG. 1c contains sections, the shape of which corresponds to that of a cycloid. Shown once more in FIGS. 2, 3 and 4 is the profile contour according to FIG. 1a. The letters and numbers in the figures indicate the following:
1: Rotors PA1 2: Rotational axes of the rotors PA1 3: Short axis of the rotors PA1 4: Long axis of the rotors PA1 5: Rolling cycle PA1 6: Profile at the base of the rotor (rotor contour within rolling cycle 5) PA1 7: Profile at the top of the rotor (rotor contour outside rolling cycle 5) PA1 8,9: Profile sections at the base PA1 11,12: Profile sections at the top PA1 13: Envelope or contour of the pumping chamber PA1 1: Rolling cycle diameter or distance between the rotational axes 2 PA1 B: Shorter diameter of the rotor (waist) PA1 C: Point of osculation of rolling cycles 5 PA1 D: Longer diameter of the rotor PA1 E1-E4: Lines of action PA1 F: Effective pumping area of the rotor PA1 Q: Cross sectional area of the pumping chamber PA1 to,t: Tangents to a "point of contact" PA1 x,y: Fixed system of coordinates referenced to the rotor (FIG. 4) PA1 xf,yf: Fixed system of coordinates referenced to the housing (FIG. 3) PA1 .rho.: Angle of rotation PA1 a (.rho.): Angle of inclination of the tangent to the profile contour at the "point of contact" of both rotors in the x/y system of coordinates.
FIGS. 2, 3 and 4 show that the profile contour of rotor 1 is composed of four profile sections at the base 8, 9 and four profile sections at the top 11, 12. Profile sections 8, 9 extend from the actual base (where the contour intersects the short rotor axis 3) to the intersect of the contour with rolling cycle 5. The four sections of the base form equal pairs (pairs 8, 8 and 9, 9) and symmetrical pairs (pairs 8, 9). The profile sections at the top extend from the intersect with long rotor axis 4 to the intersect with rolling cycle 5. The top sections also form equal pairs (pairs 11, 11 and 12, 12) and symmetrical pairs (pairs 11,12). The profile contours shown in FIGS. 1a and 2 to 4 correspond to state of the art rotors (involute), which are being used widely in vacuum technology.
At any rotor position in the pumping chamber there is always a point where they come closest. In the following this point is termed "point of contact", although the rotors do not actually come in to contact. At the "point of contact" the narrowed gap is formed by a point on the profile section of the base of the first rotor and a point on the corresponding profile section at the top of the second rotor. In a Cartesian system of x/y coordinates referenced to the rotor (FIG. 4) there is a value EQU f(.rho.)=Y(.rho.)=a(.rho.)
which corresponds to each angle of rotation .rho..
a(.rho.) is the angle of inclination of the tangent to the "point of contact" on the profile contour. For example, at an angle of rotation of .rho.=0 the inclination of tangent t.sub.0 to the "point of contact" of the profile contour is equal to 0 (FIG. 3).
during operation of the pump or while the rotor is rotating, the "point of contact" moves along a closed path.
The typical line of action for rotor profile contours according to FIGS. 1a, 2 to 4 (involute) is shown in FIG. 3 and marked as E.sub.1. It has a shape similar to a figure-of-eight with a centre which is marked C. The line of action E.sub.1 is shown in a fixed system of coordinates x.sub.f, y.sub.f, related to the stationary housing, the origin of which is located on axis 2 of a rotor. The system of coordinates xf, yf, is drawn into FIG. 3.
A characteristic quantity which describes the characteristic of a Roots pump of the described type is the efficiency of area .mu., which is defined as the ratio between four times the effective pumping area F of the rotor and the cross sectional area Q of pumping chamber 13. The volume V pumped during each half-turn of the rotors is equal to the product of effective pumping area F of the rotor and length l of pumping chamber 13, so that the following applies the amount of gas which can be theoretically pumped (pumping speed): EQU Qth=4.multidot.V.multidot.n=4.multidot.F.multidot.l.multidot.n
where n is the speed of the rotors. For a given cross sectional area Q and with increasing values of F (and thus V) the efficiency of area .mu. will increase and thus Q.sub.th. At a given pumping speed a high efficiency of area .mu. will lead to small and compact Roots vacuum pumps, with a direct effect on the material and production costs and hence the price of the pump.
A further characteristic quantity used to describe a Roots vacuum pump is volumetric efficiency .eta.. This quantity is defined as the ratio between the effectively pumped quantity of gas Q.sub.off and the Quantity of gas Q.sub.th which can be pumped theoretically. Because of the gaps which are an inherent design feature of a Roots vacuum pump of the type described here (non-contact movement of the rotors) backstreaming of gas is unavoidable and therefore Q.sub.eff is always lower than Q.sub.th. The larger the value of .eta., the better the compression characteristic of a Roots vacuum pump. A relatively high value of .eta. could for example be obtained by small gaps at the "point of contact" on the one hand and between rotors and housing of the pump chamber on the other hand. However, small gaps result in a high temperature sensitivity of the pump. The reason for this is, that the amount of heat which may be removed from the rotors rotating in the vacuum is limited. In the case of small gaps a small temperature increase of the rotors reduces the gap and thus prevents the rotors from starting up.
With respect to optimized characteristics of a Roots vacuum pump values for .mu. and .eta. which are as high as possible are very desirable.
At the same time it has to be borne in mind that complex manufacturing methods are employed especially for the rotors due to their special profile contours and the small gaps. Because of the complex manufacturing methods it has to date been usually more cost-effective to manufacture large Roots machines with sub-optimum .mu. and .eta. values, rather than smaller machines with better values for .mu. and .eta. with otherwise identical performance characteristics.
For further details on the current state of the art refer to the book by G. Niemann and H. Winter "Maschinenelemente", Vol. 2, 1985 as well as the already quoted publication CH-PS 389 817. These references show on the one hand that numerous profile contours for rotors are known (CH-PS) but which mostly not have been able to gain success in the market. On the other hand these references show that the profile contour of Roots blowers and pumps which are well established in the market are produced with the aid of roulettes (cycloids, involutes) (CH-PS 389 817, FIG. 2; "Maschinenelemente", Vol 2, p. 142). The efficiency of area .mu. of Roots pumps with such rotors hardly exceeds 50%.
Moreover, a profile contour of a rotor is disclosed in CH-PS 389 817 where the longer sides of the profile at the base are made to run in parallel (straight rotors). According to the aforementioned CH patent publication this contour makes it possible to obtain a relatively low ultimate pressure, but at the expense of a considerable reduction in the efficiency of area .mu., as the effective pumping area F of the rotor is larger in the case of rotors having a waist compared to pumps with straight rotors (compare this to the areas 9 or 32 in FIGS. 4b and 6b of CH-PS 389 817). Machines with rotor profile contours of the type proposed in CH-PS 389 817 are therefore fairly large, correspondingly heavy and consequently relatively costly.